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Icosahedron Class Documentation

Overview

Icosahedron

References

Class Documentation

Bases: Polyhedron

Icosahedron Class

Regular unit icosahedron.

calc_angle_dihedral() staticmethod

Face-edge-face angle, i.e., "dihedral angle" (approx. 138.190)

calc_angle_solid_vertex() staticmethod

Solid angle at a vertex subtended by a face (approx. 2.63455 steradians)

calc_angle_subtended(a) staticmethod

Vertex-Center-Vertex angle calc_face_angle_face_edge_face The angle between lines from the dodecahedron center to any two vertices. It is also the angle between Plateau borders at a vertex. In chemistry it is called the tetrahedral bond angle. This angle (in radians) is also the length of the circular arc on the unit sphere resulting from centrally projecting one edge of the dodecahedron to the sphere.

(approx. 63.435)

calc_area(a) staticmethod

Formula to calculate area of Icosahedron

calc_radius_circumsphere(a) staticmethod

Radius of circumsphere the radius of a circumscribed sphere (one that touches the icosahedron at all vertices)

~ 0.9510565163 * a

calc_radius_insphere(a) staticmethod

Radius of insphere that is tangent to faces The radius of an inscribed sphere (tangent to each of the icosahedron's faces) is

~ 0.7557613141 * a

calc_radius_midsphere(a) staticmethod

Radius of midsphere that is tangent to edges

while the midradius, which touches the middle of each edge, is

calc_volume(a) staticmethod

Formula to calculate volume of Icosahedron

faces() staticmethod

20 faces

vertices() staticmethod

12 principal directions in 3D space: points on an unit Icosahedron.

Vertex coordinates:

Position 1 ( 0, ±1, ±φ) (±1, ±φ, 0) (±φ, 0, ±1)

or:

Position 2 ( 0, ±φ, ±1) (±φ, ±1, 0) (±1, 0, ±φ)